Vortex Shedding from a Microsphere Oscillating in Superfluid ^4He at mK Temperatures and from a Laser Beam Moving in a Bose–Einstein Condensate

Abstract

Turbulent drag of an oscillating microsphere that is levitating in superfluid ^4He at mK temperatures, is unstable slightly above a critical velocity amplitude v_c. The lifetime tau of the turbulent state is determined by the number n of vortices shed per half-period. It is found that this number is identical to the superfluid Reynolds number. The possibility of moving a levitating sphere through superfluid ^3He at microkelvin temperatures is considered. A laser beam moving through a Bose–Einstein condensate (BEC) (as observed by other authors) also produces vortices in the BEC. In particular, in either case, a linear dependence of the shedding frequency f_v on Delta v = v - v_c is observed, where v is the velocity amplitude of the sphere or the constant velocity of the laser beam above v_c for the onset of turbulent flow: f_v = a ,Delta v, where the coefficient a is proportional to the oscillation frequency omega above some characteristic frequency omega _k and assumes a finite value for steady motion omega rightarrow 0. A relation between the superfluid Reynolds number and the superfluid Strouhal number is presented that is different from classical turbulence.